refactoring

[helm.git] / helm / software / matita / library / assembly / exadecimal.ma

diff --git a/helm/software/matita/library/assembly/exadecimal.ma b/helm/software/matita/library/assembly/exadecimal.ma
index 3a4e35da40384455eefebbd252648dbcfc9ea984..761c06c94718ce89014d63e06622198fad0d83ab 100644 (file)
--- a/helm/software/matita/library/assembly/exadecimal.ma
+++ b/helm/software/matita/library/assembly/exadecimal.ma
@@ -14,7 +14,7 @@
 
 set "baseuri" "cic:/matita/assembly/exadecimal/".
 
-include "extra.ma".
+include "assembly/extra.ma".
 
 inductive exadecimal : Type ≝
    x0: exadecimal
@@ -801,7 +801,8 @@ lemma exadecimal_of_nat_mod:
  change in ⊢ (? ? ? (? (? % ?))) with (n16 \mod 16);
  rewrite < mod_mod;
   [ apply H;
-    autobatch
+    unfold lt;
+    autobatch.
   | autobatch
   ]
 qed.
@@ -836,16 +837,19 @@ lemma nat_of_exadecimal_exadecimal_of_nat:
   ]
 qed.
 
+lemma exadecimal_of_nat_nat_of_exadecimal:
+ ∀b.exadecimal_of_nat (nat_of_exadecimal b) = b.
+ intro;
+ elim b;
+ reflexivity.
+qed.
+
 lemma plusex_ok:
  ∀b1,b2,c.
   match plusex b1 b2 c with
    [ couple r c' ⇒ b1 + b2 + nat_of_bool c = nat_of_exadecimal r + nat_of_bool c' * 16 ].
  intros;
- elim c;
- elim b1;
- elim b2;
- normalize;
- reflexivity.
+ elim b1; (elim b2; (elim c; normalize; reflexivity)).
 qed.
 
 definition xpred ≝
@@ -904,9 +908,20 @@ lemma eqex_true_to_eq: ∀b,b'. eqex b b' = true → b=b'.
  first [ reflexivity | destruct H ].
 qed.
  
+lemma eqex_false_to_not_eq: ∀b,b'. eqex b b' = false → b ≠ b'.
+ intros 2;
+ elim b 0;
+ elim b' 0;
+ simplify;
+ intro;
+ try (destruct H);
+ intro K;
+ destruct K.
+qed.
+ 
 (*
 lemma xpred_S: ∀b. xpred (exadecimal_of_nat (S b)) = exadecimal_of_nat b.
  intros;
  rewrite > exadecimal_of_nat_mod;
  rewrite > exadecimal_of_nat_mod in ⊢ (? ? ? %);
-*)
\ No newline at end of file
+*)